# Henning Thomas

• Electr. J. Comb.
• 2009
Consider the following one-player game. Starting with the empty graph on n vertices, in every step r new edges are drawn uniformly at random and inserted into the current graph. These edges have to be colored immediately with r available colors, subject to the restriction that each color is used for exactly one of these edges. The player’s goal is to avoid(More)
• CTW
• 2012
We analyze the general version of the classic guessing game Mastermind with <i>n</i> positions and <i>k</i> colors. Since the case <i>k</i> &leq; <i>n</i><sup>1 &minus; &epsiv;</sup>, &epsiv; &gt; 0 a constant, is well understood, we concentrate on larger numbers of colors. For the most prominent case <i>k</i> &equals; <i>n</i>, our results imply that(More)
• Electronic Notes in Discrete Mathematics
• 2009
We study the following two problems: i) Given a random graph Gn,m (a graph drawn uniformly at random from all graphs on n vertices with exactly m edges), can we color its edges with r colors such that no color class contains a component of size Θ(n)? ii) Given a random graph Gn,m with a random partition of its edge set into sets of size r, can we color its(More)
• Journal of Computer Science and Technology
• 2007
We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is either forbidden or permitted, and we wish to maximize the total profit. Since this optimization problem is NP-hard, we focus on approximation algorithms. We obtain fast and simple algorithms for the non-rotational scenario with(More)
• J. Comb. Theory, Ser. B
• 2011
The standard paradigm for online power of two choices problems in random graphs is the Achlioptas process. Here we consider the following natural generalization: Starting with G0 as the empty graph on n vertices, in every step a set of r edges is drawn uniformly at random from all edges that have not been drawn in previous steps. From these, one edge has to(More)
• Electronic Notes in Discrete Mathematics
• 2011
The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erdős-Rényi process (ER). It is well known that this process undergoes a phase transition at n/2 edges when, asymptotically almost surely, a linear-sized component appears. Moreover, this phase transition is continuous, i.e.,(More)
• Random Struct. Algorithms
• 2011
The standard randomization of Ramsey’s theorem [11] asks for a fixed graph F and a fixed number r of colors: for what densities p = p(n) can we asymptotically almost surely color the edges of the random graph G(n, p) with r colors without creating a monochromatic copy of F . This question was solved in full generality by Rödl and Ruciński [12, 14]. In this(More)
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